There, R.L. Moore initially denied him admission to his topology class. Wilder persisted and took the class. Moore continued to expect little of him due to his academic background and ignored him until he proved difficult theorems.

Eventually, while still studying actuarial science, Wilder solved a problem that had stumped J.R. Kline and others. When Moore heard, he urged Wilder to write it up as a thesis, and Wilder graduated with a Ph.D. in topology the same year (despite having missed deadlines for language and qualifying exams – Moore's prestige at the University of Texas superseded these requirements). In this way, Wilder became Moore's first Ph.D. student at the University of Texas in 1923.

In 1924, Wilder joined the Ohio State University as an assistant professor. Two years later, he joined the faculty of the University of Michigan, where he spent the majority of his academic career and supervised 25 doctoral theses. Wilder taught a course on the foundations of mathematics that appealed to students with non-mathematical interests and became one of the most popular courses on campus. He was a Henry Russel Lecturer. In his honor, the University of Michigan held a conference in 1966 and established a Raymond L. Wilder Professorship of Mathematics.

Wilder's mathematical writing includes more than 70 papers and three books, primarily on topology. He also maintained interests in the history and anthropology of mathematics, as evidenced not only by his popular foundations course but also by his address at the 1950 International Congress of Mathematicians on "The Cultural Basis of Mathematics" and his 1969 American Mathematical Society (AMS) Gibbs Lecture on "Trends and Social Implications of Research."